Herman te Riele

Last updated

Hermanus Johannes Joseph te Riele (born 5 January 1947) is a Dutch mathematician at CWI in Amsterdam with a specialization in computational number theory. He is known for proving the correctness of the Riemann hypothesis for the first 1.5 billion non-trivial zeros of the Riemann zeta function with Jan van de Lune and Dik Winter, for disproving the Mertens conjecture with Andrew Odlyzko, and for factoring large numbers of world record size. In 1987, he found a new upper bound for π(x) Li(x).

In 1970, Te Riele received an engineer's degree in mathematical engineering from Delft University of Technology and, in 1976, a PhD degree in mathematics and physics from University of Amsterdam (1976).

Related Research Articles

The de Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles Michael Newman, is a mathematical constant defined via the zeros of a certain function H(λ,z), where λ is a real parameter and z is a complex variable. More precisely,

The Liouville lambda function, denoted by λ(n) and named after Joseph Liouville, is an important arithmetic function. Its value is +1 if n is the product of an even number of prime numbers, and −1 if it is the product of an odd number of primes.

<span class="mw-page-title-main">Goldbach's weak conjecture</span> Solved conjecture about prime numbers

In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that

In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number for which

<span class="mw-page-title-main">Prime-counting function</span> Function representing the number of primes less than or equal to a given number

In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by π(x) (unrelated to the number π).

<span class="mw-page-title-main">Mertens conjecture</span> Disproved mathematical conjecture

In mathematics, the Mertens conjecture is the statement that the Mertens function is bounded by . Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite, and again in print by Franz Mertens, and disproved by Andrew Odlyzko and Herman te Riele . It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor.

<span class="mw-page-title-main">Mertens function</span> Summatory function of the Möbius function

In number theory, the Mertens function is defined for all positive integers n as

In mathematics, the Gauss class number problem, as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields having class number n. It is named after Carl Friedrich Gauss. It can also be stated in terms of discriminants. There are related questions for real quadratic fields and for the behavior as .

Richard Peirce Brent is an Australian mathematician and computer scientist. He is an emeritus professor at the Australian National University. From March 2005 to March 2010 he was a Federation Fellow at the Australian National University. His research interests include number theory, random number generators, computer architecture, and analysis of algorithms.

John Lewis Selfridge, was an American mathematician who contributed to the fields of analytic number theory, computational number theory, and combinatorics.

In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf about the rate of growth of the Riemann zeta function on the critical line. This hypothesis is implied by the Riemann hypothesis. It says that for any ε > 0,

<span class="mw-page-title-main">Andrew Odlyzko</span> American mathematician

Andrew Michael Odlyzko is a Polish-American mathematician and a former head of the University of Minnesota's Digital Technology Center and of the Minnesota Supercomputing Institute. He began his career in 1975 at Bell Telephone Laboratories, where he stayed for 26 years before joining the University of Minnesota in 2001.

In mathematics, the Kummer–Vandiver conjecture, or Vandiver conjecture, states that a prime p does not divide the class number hK of the maximal real subfield of the p-th cyclotomic field. The conjecture was first made by Ernst Kummer on 28 December 1849 and 24 April 1853 in letters to Leopold Kronecker, reprinted in, and independently rediscovered around 1920 by Philipp Furtwängler and Harry Vandiver,

<span class="mw-page-title-main">Pólya conjecture</span> Disproved conjecture in number theory

In number theory, the Pólya conjecture stated that "most" of the natural numbers less than any given number have an odd number of prime factors. The conjecture was set forth by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove. Though mathematicians typically refer to this statement as the Pólya conjecture, Pólya never actually conjectured that the statement was true; rather, he showed that the truth of the statement would imply the Riemann hypothesis. For this reason, it is more accurately called "Pólya's problem".

<span class="mw-page-title-main">Daniel Shanks</span> American mathematician

Daniel Charles Shanks was an American mathematician who worked primarily in numerical analysis and number theory. He was the first person to compute π to 100,000 decimal places.

<span class="mw-page-title-main">Riemann hypothesis</span> Conjecture on zeros of the zeta function

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann, after whom it is named.

In number theory, Gillies' conjecture is a conjecture about the distribution of prime divisors of Mersenne numbers and was made by Donald B. Gillies in a 1964 paper in which he also announced the discovery of three new Mersenne primes. The conjecture is a specialization of the prime number theorem and is a refinement of conjectures due to I. J. Good and Daniel Shanks. The conjecture remains an open problem: several papers give empirical support, but it disagrees with the widely accepted Lenstra–Pomerance–Wagstaff conjecture.

In number theory, the Erdős–Moser equation is

<span class="mw-page-title-main">Andrew Sutherland (mathematician)</span>

Andrew Victor Sutherland is an American mathematician and Principal Research Scientist at the Massachusetts Institute of Technology. His research focuses on computational aspects of number theory and arithmetic geometry. He is known for his contributions to several projects involving large scale computations, including the Polymath project on bounded gaps between primes, the L-functions and Modular Forms Database, the sums of three cubes project, and the computation and classification of Sato-Tate distributions.

References